Area of polygon? 16cm, 7cm, 6cm,5cm, 4cm
To find the area of a polygon with sides of different lengths, you can use the formula for the area of a trapezoid.
First, calculate the semi-perimeter of the polygon by adding all the side lengths and dividing by 2:
Perimeter = 16cm + 7cm + 6cm + 5cm + 4cm = 38cm
Semi-perimeter = 38cm / 2 = 19cm
Next, use the formula for the area of a trapezoid:
Area = [(a + b) / 2] * h
In this case, we can consider the sides 16cm and 4cm as the bases of the trapezoid, and the height h as the distance between the two bases.
a = 16cm, b = 4cm, h = ?
To find the height (h), we can use the equation of the Pythagorean theorem:
h^2 = (5cm)^2 - ((16cm - 4cm) / 2)^2
h^2 = 25cm^2 - 36cm^2
h^2 = 25cm^2 - 9cm^2
h^2 = 16cm^2
h = 4cm
Then, plug in the values for a, b, and h into the formula:
Area = [(16cm + 4cm) / 2] * 4cm
Area = (20cm / 2) * 4cm
Area = 10cm * 4cm
Area = 40cm^2
So, the area of the polygon is 40 square centimeters.